Sorry if it sounds like I am being a dick (it is not my intention) but it sounds like she needs to watch where she is putting her feet. By all means ask the school to look at it but there is no way I would expect money from a school for me being clumsy.
Nothing to do with being clumsy, although I agree that you shouldn’t be chasing compo. In this instance , i would rather the money go to fixing the problem.
I would take dimensions of the stair going and risers to identify if there is a problem, then find out if it has been officially reported as an error.
Is it a new school ? Or a new staircase in the school ? In any case, if there is a serious flaw like that , then it should be made out of bounds until it is fixed. Falling up the stairs is one thing, falling down them could be quite another.
One of the things I supply are steel staircases. They have got to be bang on at fabrication / erection stage or they do not go out the door.